A370087 Expansion of e.g.f. exp( Sum_{k>=1} (3*k)!/k! * (x/6)^k/k ).

1, 1, 11, 591, 95001, 34158801, 23091398451, 26242572454911, 46391926016144241, 120482101765570623201, 439905589366043539453851, 2180755271892747703236167151, 14267395360715456605222995351561, 120323721300147111590970495558478641

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Formula

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} (3*k)!/6^k * binomial(n,k) * a(n-k).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, (3*k)!/k!*(x/6)^k/k))))

Crossrefs

Cf. A014606, A370085.

Sequence in context: A376460 A265978 A263184 * A288326 A260583 A079915

Adjacent sequences: A370084 A370085 A370086 * A370088 A370089 A370090

Keyword

nonn

Author

Seiichi Manyama, Feb 08 2024

Status

approved